Thick tuna steaks are not just for grilling. The stovetop technique here is quick and convenient. You use one big skillet for browning the fish steaks, make a simple (yet complex-tasting) sauce, and put the two together for a final brief braise that marries the flavors perfectly. This is the true alla Genovese method.
If you prefer grilling to pan-cooking, however, you can certainly omit the first step of flouring and frying the steaks, and make the sauce separately. Use a smaller saucepan in this case, preparing the sauce as in the recipe, starting with the sauté of garlic, anchovies, and porcini in 2 tablespoons olive oil. (Use the other 3 tablespoons olive oil, and 1/2 teaspoon salt, to season the fish before grilling.)
One advantage of a separate sauce is that it can be finished ahead of time, so when your guests arrive you only have to fire up the grill and cook the fish. And you'll find it delicious with bass, codfish, or salmon as well as tuna. In fact, this sauce is so good; I suggest you have a good slab of focaccia to mop up the pan.

Sprinkle salt all over the tuna steaks, using about 1/2 teaspoon salt in all. Dredge each steak in the flour, coating both sides, and shake off the excess. Pour 4 tablespoons of the olive oil into the skillet, and set it over medium-high heat. When the oil is hot, lay all the tuna in the pan, and sauté on the first side for about 1 minute, just until browned. Flip the steaks over, and brown the second side, another minute or so, then take the pan off the heat. Transfer the tuna to a platter, and keep in a warm place while you make the sauce.

Lift the rehydrated porcini pieces from the soaking water (reserve it), and chop them fine. Pour the remaining 2 tablespoons olive oil into the skillet, set it over medium-high heat, toss in the garlic cloves, then stir in the chopped anchovy and porcini. Cook and stir until everything is sizzling nicely, then pour in the white wine, lemon juice, and porcini water (leaving behind any sediment). Add the thyme sprigs, and season with the remaining salt. Bring the sauce to a boil, and cook until reduced by about half.

When the sauce has thickened to a consistency you like, arrange the tuna steaks in the skillet again, and pour in any juices from the platter. Heat for a minute in the bubbling sauce, then turn the steaks over and cook briefly on the second side. The tuna should still be rare at this point; if you prefer your steaks better done, simply let them cook in the sauce longer.

Just before serving, drop the 2 tablespoons butter (or extra-virgin olive oil, if you prefer) into the pan, between the steaks, and stir it into the sauce as a final enrichment. Turn off the heat, and stir in the parsley. Serve the steaks on dinner plates, spooning sauce over them, or arrange them on a serving platter, with the sauce on top.

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